Is it possible to move parts of a model along the selected normals?
You can set the Transform orientation to Normal in 3D view > Header:



This will align the Z to the normal of the selected element. (Or in the case of multiple selected elements, the average of the normals of all selected elements):



Note that pressing GZ will still move the selection along the global coordinates, to move the selection along the orientation set with Transform Orientation you need to press the axis key twice (so GZZ).